1. Field of the Invention
The present invention relates to an apparatus for processing a digital signal and its method. More particularly, the present invention relates to the apparatus and method for processing a digital signal, which avoids aliasing occurring during converting a digital signal into an analog signal.
2. Background of the Invention
In general, digital equipment such as compact disc (CD) players or digital audio tape (DAT) players use a D/A (digital do analog) converter to convert a digital audio signal readout from a recording medium into an analog audio signal as a reproducing output signal. The image components occur at both sides of a certain frequency that is the integral multiple of an original sampling frequency when the digital audio signal is converted into the analog audio signal. The image components contained aliasing interference. In such digital equipment, it is necessary to avoid aliasing when the digital audio signal is converted into the analog audio signal. It is possible to avoid aliasing by eliminating image components.
For example, in the CD players in early days, aliasing was avoided utilizing an analog low pass filter. However, the technology has been recently established for massproducing digital filters. The analog filter now becomes more expensive than digital one. In addition, the analog filter having a sharp filtering characteristics deteriorates the quality of the reproducing sound. Therefore, aliasing is presently avoided by use of a digital filter.
Most recently, the sampling frequency (fs) is converted into eight times sampling frequency (8fs) so that image components may be eliminated in the audio frequency band. It is aimed to perform enough suppression of components out of the band and also relax the specification of the analog filter after the D/A converter. The digital filter arrangement has been proposed to convert the sampling frequency (fs) into the eight times sampling frequency (8fs). As shown in FIG. 1, FIR (Finite Impulse Response) filters 21, 22 and 23 are connected in series. The FIR filter 21 converts the sampling frequency (fs) supplied from an input terminal 20 into (2fs). The FIR filter 22 converts the sampling frequency (2fs) into (4fs). The FIR filter 23 converts the sampling frequency (4fs) into (8fs). Consequently, the signal (8fs) is outputted from an output terminal 24. Rather than converting the sampling frequency (fs) into (8fs) at one step conversion process, the step-by-step conversion process as aforesaid is preferred due to better efficiency. The FIR filters 21, 22 and 23 have a linear phase.
The eight times sampling frequency is obtained by connecting three FIR filters in series. These FIR filters have linear phase and convert the sampling frequency of the input signal into a twice sampling frequency. As a result, it is possible to use the well-known technology that the number of operations can be reduced when the cut-off frequency is set to a half frequency of the Nyquist frequency. The hardware can be therefore simplified compared with converting the sampling frequency into the eight times one in a one step conversion process.
Three FIR filters are connected in series, each of which has the linear phase and converts the sampling frequency (fs) of the input signal into the twice one, to finally obtain the eight times sampling frequency. At this time, operations of addition and multiplication at each of FIR filters can be performed by a single operation part with time division processing.
As a result, the allowable input word length of each FIR filters become the same word length, and so does the output word length of each FIR filters. In general, the output word length becomes longer than the allowable input word length in the filtering process. As shown in FIG. 2, a rounding process unit 25 (RPU) is therefore connected between the FIR filter 21 and 22 shown in FIG. 1. The rounding process unit 25 converts the output word length of the FIR filter 21 rounded so that it can be suitable for the allowable word length of the FIR filter 22.
A rounding error which is generated during this rounding process is mixed with the output signal from the FIR filter 21. The output signal of the rounding process unit 25 is then filtered by the FIR filter 22 with the twice sampling frequency (4fs). The filtering output signal can be outputted through an output terminal 26.
The spectrum of the signal at the locations A, B, C and D shown in FIG. 2 are shown and explained below with FIGS. 3A through 3D. The spectrum of the original signal shown in FIG. 3A is band-limited by the FIR filter 21 which has the filtering characteristics as shown by dotted lines in FIG. 3B. At this time, the sampling frequency of the original signal is converted into twice the sampling frequency by the FIR filter 21. Since the word length of the output signal outputted from the FIR filter 21 becomes longer than the word length of the input signal inputted in the FIR filter 21 in the general filtering process as explained, the limitation of the word length at the input stage of the FIR filter 22 may cause some problem. Therefore, the word length of the output data from the FIR filter 21 is rounded by the rounding process unit 25. The rounding error, i.e., the re-quantization error, is generated by the rounding process. The rounding error, there-quantization error, is mixed with the original signal as shown by hatched portion in FIG. 3C. The output signal of the rounding process unit 25 as shown in FIG. 3C has the word length within the allowable input word length of the FIR filter 22. The FIR filter 22 converts the sampling frequency into (4fs). Since the re-quantization error is mixed with the original signal as 25 described above, the original signal mixed with the re-quantization error is outputted through the output terminal 26.
When the allowable input word length are all same in each FIR filters 21, 22 and 23 shown in FIG. 1, the input signal is limited to the word length at the input stage of the FIR filters 22 and 23. As a result, the output signal mixed with the rounding error is outputted from the output stage of the FIR filter 22 and 23, since the rounding error, the re-quantization error, occurred at the input stage of the FIR filter 22, 23.
The output signal mixed with the re-quantization error is not outputted, if each of FIR filters 21, 22 and 23 is constituted as independent operation elements. However, in this case, the digital signal operation apparatus becomes a more expensive apparatus.
It is also considered to convert the input word length to one shorter for the FIR filter 21 and 22 so that the re-quantization error may become small enough at the input stage of the FIR filter 23. However, this wastes the original ability of the FIR filters.